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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox MOS}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{MOS intro|Other Names=m-chromatic}} |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-10-15 12:49:16 UTC</tt>.<br>
| |
| : The original revision id was <tt>373189022</tt>.<br>
| |
| : The revision comment was: <tt></tt><br>
| |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| |
| <h4>Original Wikitext content:</h4>
| |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">This is the MOS pattern of the [[Meantone family|meantone]] chromatic scale, which is the only notable harmonic entropy minimum in this range of possible scales. In meantone, "diatonic" semitones (~16/15), such as appear in the [[5L 2s|diatonic scale]], for example B-C, are larger than "chromatic" semitones (~25/24), the intervals by which flats and sharps alter pitches.
| |
|
| |
|
| The meantone chromatic scale is [[Rothenberg propriety|proper]].
| | 7L 5s represents the chromatic scale of [[meantone]], or meantone chromatic scale. Such scales are characterized by having a small step ([[diatonic semitone]]) that is larger than the [[chroma]] ([[chromatic semitone]]), the reverse of [[5L 7s]]. |
| ||||||||||~ Generator ||~ ||~ in cents ||~ Comments ||
| |
| ||= 3\7 ||= ||= ||= ||= || ||= 514.286 ||= ||
| |
| || || || || || || 20/47 || 510.638 || ||
| |
| ||= ||= ||= ||= ||= 17\40 || ||= 510.000 ||= ||
| |
| || || || || || || 31/73 || 509.589 || ||
| |
| ||= ||= ||= ||= 14\33 ||= || ||= 509.091 ||= ||
| |
| || || || || || || 39/92 || 508.696 || ||
| |
| ||= ||= ||= ||= ||= 25\59 || ||= 508.475 ||= ||
| |
| || || || || || || 36/85 || 508.235 || ||
| |
| ||= ||= ||= 11\26 ||= ||= || ||= 507.692 ||= ||
| |
| || || || || || || 41/97 || 507.216 || ||
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| ||= ||= ||= ||= ||= 30\71 || ||= 507.042 ||= Flattone ||
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| || || || || || || 49/116 || 506.897 || ||
| |
| ||= ||= ||= ||= 19\45 ||= || ||= 506.667 ||= Flattone ||
| |
| || || || || || || 46/109 || 506.422 || ||
| |
| ||= ||= ||= ||= ||= 27\64 || ||= 506.250 ||= Flattone ||
| |
| || || || || || || 35/83 || 506.024 || ||
| |
| ||= ||= 8\19 ||= ||= ||= || ||= 505.263 ||= Boundary of propriety: generators
| |
| smaller than this are proper ||
| |
| || || || || || || 37/88 || 504.545 ||= LucyTuning ||
| |
| ||= ||= ||= ||= ||= 29\69 || ||= 504.348 ||= ||
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| || || || || || || 50/119 || 504.202 || ||
| |
| ||= ||= ||= ||= 21\50 ||= || ||= 504.000 ||= ||
| |
| || || || || || || 55\131 || 503.817 ||= Golden meantone ||
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| ||= ||= ||= ||= ||= 34\81 || ||= 503.704 ||= Optimal meantone is around here ||
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| || || || || || || 47/112 || 503.571 || ||
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| ||= ||= ||= 13\31 ||= ||= || ||= 503.226 ||= Optimal rank range (L/s=3/2) ||
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| || || || || || || 44/105 || 502.857 || ||
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| ||= ||= ||= ||= ||= 31\74 || ||= 502.703 ||= ||
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| || || || || || || 49/117 || 502.564 || ||
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| ||= ||= ||= ||= 18\43 ||= || ||= 502.326 ||= ||
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| || || || || || || 41/98 || 502.041 || ||
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| ||= ||= ||= ||= ||= 23\55 || ||= 501.818 ||= ||
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| || || || || || || 28/67 || 501.493 || ||
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| ||= 5\12 ||= ||= ||= ||= || ||= 500.000 ||= ||</pre></div>
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| <h4>Original HTML content:</h4>
| |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>7L 5s</title></head><body>This is the MOS pattern of the <a class="wiki_link" href="/Meantone%20family">meantone</a> chromatic scale, which is the only notable harmonic entropy minimum in this range of possible scales. In meantone, &quot;diatonic&quot; semitones (~16/15), such as appear in the <a class="wiki_link" href="/5L%202s">diatonic scale</a>, for example B-C, are larger than &quot;chromatic&quot; semitones (~25/24), the intervals by which flats and sharps alter pitches.<br />
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| <br />
| |
| The meantone chromatic scale is <a class="wiki_link" href="/Rothenberg%20propriety">proper</a>.<br />
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|
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|
| | Meantone is the only notable harmonic entropy minimum. |
|
| |
|
| <table class="wiki_table">
| | == Scale properties == |
| <tr>
| | {{TAMNAMS use}} |
| <th colspan="5">Generator<br />
| |
| </th>
| |
| <th><br />
| |
| </th>
| |
| <th>in cents<br />
| |
| </th>
| |
| <th>Comments<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">3\7<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">514.286<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>20/47<br />
| |
| </td>
| |
| <td>510.638<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">17\40<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">510.000<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>31/73<br />
| |
| </td>
| |
| <td>509.589<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">14\33<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">509.091<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>39/92<br />
| |
| </td>
| |
| <td>508.696<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">25\59<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">508.475<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>36/85<br />
| |
| </td>
| |
| <td>508.235<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">11\26<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">507.692<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>41/97<br />
| |
| </td>
| |
| <td>507.216<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">30\71<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">507.042<br />
| |
| </td>
| |
| <td style="text-align: center;">Flattone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>49/116<br />
| |
| </td>
| |
| <td>506.897<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">19\45<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">506.667<br />
| |
| </td>
| |
| <td style="text-align: center;">Flattone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
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| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
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| </td>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>46/109<br />
| |
| </td>
| |
| <td>506.422<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
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| <td style="text-align: center;"><br />
| |
| </td>
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| <td style="text-align: center;">27\64<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">506.250<br />
| |
| </td>
| |
| <td style="text-align: center;">Flattone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
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| </td>
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| <td><br />
| |
| </td>
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| <td><br />
| |
| </td>
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| <td><br />
| |
| </td>
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| <td>35/83<br />
| |
| </td>
| |
| <td>506.024<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">8\19<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
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| <td style="text-align: center;"><br />
| |
| </td>
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| <td style="text-align: center;"><br />
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| </td>
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| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">505.263<br />
| |
| </td>
| |
| <td style="text-align: center;">Boundary of propriety: generators<br />
| |
| smaller than this are proper<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>37/88<br />
| |
| </td>
| |
| <td>504.545<br />
| |
| </td>
| |
| <td style="text-align: center;">LucyTuning<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
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| <td style="text-align: center;"><br />
| |
| </td>
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| <td style="text-align: center;"><br />
| |
| </td>
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| <td style="text-align: center;"><br />
| |
| </td>
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| <td style="text-align: center;">29\69<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">504.348<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>50/119<br />
| |
| </td>
| |
| <td>504.202<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
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| <td style="text-align: center;"><br />
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| </td>
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| <td style="text-align: center;"><br />
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| </td>
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| <td style="text-align: center;">21\50<br />
| |
| </td>
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| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
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| <td style="text-align: center;">504.000<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
| |
| </td>
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| <td>55\131<br />
| |
| </td>
| |
| <td>503.817<br />
| |
| </td>
| |
| <td style="text-align: center;">Golden meantone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">34\81<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">503.704<br />
| |
| </td>
| |
| <td style="text-align: center;">Optimal meantone is around here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
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| <td><br />
| |
| </td>
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| <td><br />
| |
| </td>
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| <td>47/112<br />
| |
| </td>
| |
| <td>503.571<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">13\31<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">503.226<br />
| |
| </td>
| |
| <td style="text-align: center;">Optimal rank range (L/s=3/2)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>44/105<br />
| |
| </td>
| |
| <td>502.857<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">31\74<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">502.703<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>49/117<br />
| |
| </td>
| |
| <td>502.564<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">18\43<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">502.326<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>41/98<br />
| |
| </td>
| |
| <td>502.041<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">23\55<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">501.818<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>28/67<br />
| |
| </td>
| |
| <td>501.493<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">5\12<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">500.000<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | === Intervals === |
| | {{MOS intervals}} |
| | |
| | === Generator chain === |
| | {{MOS genchain}} |
| | |
| | === Modes === |
| | {{MOS mode degrees}} |
| | |
| | === Proposed names === |
| | Both [[User:Eliora|Eliora]] and [[User:Ganaram inukshuk|Ganaram]] have independently proposed mode names based on names of the months. The former scheme uses mode names from the Gregorian calendar using cyclic order, starting with January assigned to the step pattern LsLsLsLLsLsL due to positioning of 31-day and 30-day months, with successive rotations assigned to successive months. The latter scheme is based on month names from the Roman calendar, starting with Mensis Martius as the brightest mode, with successive month names for each mode by descending brightness. |
| | |
| | {{MOS modes |
| | | Table Headers= |
| | Mode names<br>(by [[User:Eliora|Eliora]]) $ |
| | Mode names<br>(by [[User:Ganaram inukshuk|Ganaram]]) |
| | | Table Entries= |
| | July $ |
| | Martian $ |
| | December $ |
| | Aprilian $ |
| | May $ |
| | Maian $ |
| | October $ |
| | Junian $ |
| | March $ |
| | Quintillian <br>Julian $ |
| | August $ |
| | Sextilian <br>Augustan $ |
| | January $ |
| | Septembian $ |
| | June $ |
| | Octobian $ |
| | November $ |
| | Novembian $ |
| | April $ |
| | Decembian $ |
| | September $ |
| | Janian $ |
| | February $ |
| | Februan $ |
| | }} |
| | |
| | == Scales == |
| | * [[Meaneb471a]] – an equal beating tuning of meantone |
| | * [[Meantone12]] – 31edo tuning |
| | * [[Ratwolf]] – 20/13 wolf fifth tuning of meantone |
| | * [[Meaneb471]] – the other equal beating tuning of meantone |
| | * [[Flattone12]] – 13-limit POTE tuning of flattone |
| | |
| | == Scale tree == |
| | {{MOS tuning spectrum |
| | | 4/3 = Meantone / [[meridetone]] |
| | | 7/5 = Meantone / [[huygens]] / [[grosstone]] |
| | | 13/8 = [[Golden meantone]] (503.7855{{c}}) |
| | | 8/5 = [[Meantone]] |
| | | 5/3 = Meantone / [[meanpop]] |
| | | 5/2 = ↕ [[Flattone]] |
| | | 13/5 = Golden flattone (506.9365{{c}}) |
| | }} |
| | |
| | [[Category:12-tone scales]] |
| | [[Category:M-chromatic| ]]<!-- main article --> |
| | [[Category:Chromatic scales]] |